Problem: What is the degree of the polynomial $(4 +5x^3 +100 +2\pi x^4 + \sqrt{10}x^4 +9)$?
This polynomial is not written in standard form.  However, we don't need to write it in standard form, nor do we need to pay attention to the coefficients.  We just look for the exponents on $x$.  We have an $x^4$ term and no other term of higher degree, so $\boxed{4}$ is the degree of the polynomial.